Creating a function based on specific values and derivatives.

Question

The specific question asks me to sketch a possible graph with the following 4 conditions:

1. F'(x)>0 on -2<x<1
2. F'(x)<0 on x<-2 and x>1
3. F(-2)=-3
4. F(1)=4

Now I know how to get the first two on their own, but the problem comes in trying to find an equation that will allow both the first and second pair of conditions to be realized. Is there a way to derive an equation from these conditions without creating an antiderivative, and then modifying it and guessing whether or not it will work?